Related papers: A trace formula for the index of B-Fredholm operat…

The aim of this paper is to develop a systematic B-Fredholm theory in semiprime Banach algebras. We first generalize Smyth's important punctured neighbourhood theorem to B-Fredholm elements. Then using this result, we investigate the local…

We prove the formula for the traces of certain class of operators in bosonic and fermionic Fock spaces. Vertex operators belong to this class. Traces of vertex operators can be used for calculation of correlation functions and formfactors…

Given a (not necessarily continuous) homomorphism between Banach algebras $\T\colon\A\to\B$, an element $a\in\A$ will be said to be B-Fredholm (respectively generalized B-Fredholm) relative to $\T$, if $\T(a)\in \B$ is Drazin invertible…

While in \cite{HB} we studied classes of Fredholm-type operators defined by the homomorphism $\Pi$ from $L(X)$ onto the Calkin algebra $\mathcal{C}(X)$, $X$ being a Banach space, we study in this paper two classes of Fredholm-type operators…

We consider an action of the real line on a C*-algebra for which there is a centre-valued invariant trace. We define a family of Toeplitz operators with symbols in the original algebra. When the symbol is invertible, the Toeplitz operator…

Let $X$ a Banach space and $T$ a bounded linear operator on $X.$ We denote by $S(T)$ the set of all $\lambda \in \cit$ such that $T$ does not have the single-valued extension property at $\lambda$. In this note we prove equality up to…

In this paper we study operators originated from semi-B-Fredholm theory and as a consequence we get some results regarding boundaries and connected hulls of the corresponding spectra. In particular, we prove that a bounded linear operator…

The index of a pseudo B-Fredholm operator will be defined and generalize the usual index of a B-Fredholm operator. This concept will be used to extend some known results in Fredholm's theory. Among other results, the nullity, the…

To complete the study of Fredholm type operators of [10] and [11], we define in this paper the classes of left and right semi-B-Fredholm operators (Definition 3.1). Then, we prove that an operator $T \in L(X), X$ being a Banach space, is a…

We prove that a first order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on the real line with values in a reflexive Banach space if and only if the corresponding strongly continuous…

We compute the Fredholm index, ${\rm ind}(D_A)$, of the operator $D_A = (d/dt) + A$ on $L^2(\mathbb{R};\mathcal{H})$ associated with the operator path $\{A(t)\}_{t=-\infty}^{\infty}$, where $(A f)(t) = A(t) f(t)$ for a.e. $t\in\mathbb{R}$,…

Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…

We introduce an appropriate notion of trace in the setting of quaternionic linear operators, arising from the well-known companion matrices. We then use this notion to define the quaternionic Fredholm determinant of trace-class operators in…

The aim of this note is to generalize the notion of Fredholm operator to an arbitrary $C^*$-algebra. Namely, we define "finite type" elements in an axiomatic way, and also we define Fredholm type element $a$ as such element of a given…

We extend the classical trace (and determinant) known for the integral operators $$ ({\mathcal I}+)\int_{[0,1)^N}{\bf A}({\bf k},{\bf x}){\bf u}({\bf x})d{\bf x} $$ with matrix-valued kernels ${\bf A}$ to the operators of the form $$…

We define here a pseudo B-Fredholm operator as an operator such that 0 is isolated in its essential spectrum, then we prove that an operator $T$ is pseudo- B-Fredholm if and only if $T = R + F$ where $R$ is a Riesz operator and $F$ is a…

In this paper, we define an analytical index for a continuous family of Fredholm operators parameterized by a topological space $\mathbb{X}$ into a Hilbert space $H,$ as a sequence of integers, extending naturally the usual definition of…

In this paper, we extend Fredholm theory in von Neumann algebras established by Breuer in [5] and [6] to spectral Fredholm theory. We consider 2 by 2 upper triangular operator matrices with coefficients in a von Neumann algebra and give the…

A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory…

We consider Toeplitz and Hankel operators with piecewise continuous generating functions on $l^p$-spaces and the Banach algebra generated by them. The goal of this paper is to provide a transparent symbol calculus for the Fredholm property…